This drawing shows how forming planets drew gas to themselves.
Click on image for full size
Image from: The New Solar System
How a proto-planet sweeps up nearby material
As shown in this picture, while they were forming in the solar nebula, the nuclei of the protoplanets drew material to themselves from the cloud of gas and dust around them. The bigger a protoplanets was the more gaseous material it was able to attract to itself.
Big protoplanets such as Neptune were positioned far out from the protosun in the primordial nebula where the concentration of gas was quite low. Therefore Neptune was not able to sweep up as much gas as other gas giants like Jupiter and Saturn.
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